The Newtonian constant of gravitation, $G$, stands out in the landscape of
the most common fundamental constants owing to its surprisingly large relative
uncertainty, which is attributable mostly to the dispersion of the values
measured for it in different experiments.
This study focuses on a set of measurements of $G$ that are mutually
inconsistent, in the sense that the dispersion of the measured values is
significantly larger than what their reported uncertainties suggest that it
should be. Furthermore, there is a loosely defined group of measured values
that lie fairly close to a consensus value that may be derived from all the
measurement results, and then there are one or more groups with measured values
farther away from the consensus value, some higher, others lower.
This same general pattern is often observed in many interlaboratory studies
and meta-analyses. In the conventional treatments of such data, the mutual
inconsistency is addressed by inflating the reported uncertainties, either
multiplicatively, or by the addition of random effects, both reflecting the
presence of dark uncertainty. The former approach is often used by CODATA and
by the Particle Data Group, and the latter is common in medical meta-analysis
and in metrology.
We propose a new procedure for consensus building that models the results
using latent clusters with different shades of dark uncertainty, which assigns
a customized amount of dark uncertainty to each measured value, as a mixture of
those shades, and does so taking into account both the placement of the
measured values relative to the consensus value, and the reported
uncertainties. We demonstrate this procedure by deriving a new estimate for
$G$, as a consensus value $G = 6.67408 \times 10^{-11} \,\text{m}^{-3} \,
\text{kg}^{-1} \, \text{s}^{-2}$, with $u(G) = 0.00024 \times 10^{-11}
\,\text{m}^{-3} \, \text{kg}^{-1} \, \text{s}^{-2}$.

Engineering simulators used for steady-state multiphase pipe flows are
commonly utilized to predict pressure drop. Such simulators are typically based
on either empirical correlations or first-principles mechanistic models. The
simulators allow evaluating the pressure drop in multiphase pipe flow with
acceptable accuracy. However, the only shortcoming of these correlations and
mechanistic models is their applicability. In order to extend the applicability
and the accuracy of the existing accessible methods, a method of pressure drop
calculation in the pipeline is proposed. The method is based on well
segmentation and calculation of the pressure gradient in each segment using
three surrogate models based on Machine Learning algorithms trained on a
representative lab data set from the open literature. The first model predicts
the value of a liquid holdup in the segment, the second one determines the flow
pattern, and the third one is used to estimate the pressure gradient. To build
these models, several ML algorithms are trained such as Random Forest, Gradient
Boosting Decision Trees, Support Vector Machine, and Artificial Neural Network,
and their predictive abilities are cross-compared. The proposed method for
pressure gradient calculation yields $R^2 = 0.95$ by using the Gradient
Boosting algorithm as compared with $R^2 = 0.92$ in case of Mukherjee and Brill
correlation and $R^2 = 0.91$ when a combination of Ansari and Xiao mechanistic
models is utilized. The method for pressure drop prediction is also validated
on three real field cases. Validation indicates that the proposed model yields
the following coefficients of determination: $R^2 = 0.806, 0.815$ and 0.99 as
compared with the highest values obtained by commonly used techniques: $R^2 =
0.82$ (Beggs and Brill correlation), $R^2 = 0.823$ (Mukherjee and Brill
correlation) and $R^2 = 0.98$ (Beggs and Brill correlation).

Focus anisoplanatism is a significant measurement error when using one single
laser guide star (LGS) in an Adaptive Optics (AO) system, especially for the
next generation of extremely large telescopes. An alternative LGS
configuration, called Projected Pupil Plane Pattern (PPPP) solves this problem
by launching a collimated laser beam across the full pupil of the telescope. If
using a linear, modal reconstructor, the high laser power requirement
($\sim1000\,\mbox{W}$) renders PPPP uncompetitive with Laser Tomography AO.
This work discusses easing the laser power requirements by using an artificial
Neural Network (NN) as a non-linear reconstructor. We find that the non-linear
NN reduces the required measurement signal-to-noise ratio (SNR) significantly
to reduce PPPP laser power requirements to $\sim200\,\mbox{W}$ for useful
residual wavefront error (WFE). At this power level, the WFE becomes 160\,nm
root mean square (RMS) and 125\,nm RMS when $r_0=0.098$\,m and $0.171$\,m
respectively for turbulence profiles which are representative of conditions at
the ESO Paranal observatory. In addition, it is shown that as a non-linear
reconstructor, a NN can perform useful wavefront sensing using a beam-profile
from one height as the input instead of the two profiles required as a minimum
by the linear reconstructor.